Produkti suma kvadrata

master's thesis

• Title (english): Products sum squared
• Author: Maja Kupinić
• Mentor: Sonja Žunar (mentor)
• Mentor: Goran Muić (sumentor)
• Committee member: Sonja Žunar (predsjednik povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Committee member: Boris Širola (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-07-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu opisani su konkretni primjeri i rezultati vezani za produkte suma kvadrata. Kroz povijest su otkriveni identiteti koji vrijede za određeni prirodan broj \(n\) u kojima je zbroj \(n\) kvadrata pomnožen sa zbrojem \(n\) kvadrata opet zbroj \(n\) kvadrata. Proučavanjem tih produkata suma kvadrata dokazana su dva značajna teorema, Hurwitzov (1; 2; 4; 8)- teorem i Pfisterov teorem o sumama kvadrata, koji su glavna tema ovog rada. Za njihovo dokazivanje potrebni su pomoćni rezultati koji se stoga pojavljuju u radu. Također, opisane su i neke primjene tih teorema.

Abstract (english)

In this thesis, specific examples and results related to the products of the sum of squares are described. Through the history, there have been discovered identities that are valid for a certain natural number \(n\) by which a sum of \(n\) squares multiplied by another sum of \(n\) squares is again a sum of \(n\) squares. By studying these products of sums of squares, two significant theorems have been proved, Hurwitz’s (1; 2; 4; 8)-theorem and Pfister’s theorem on sums of squares, which are the main topic of this thesis. To prove them, we needed auxiliary results so they therefore appear in the thesis. Moreover, some applications of these theorems are described.

• Keywords: Hurwitzov teorem; Pfisterov teorem o sumama kvadrata
• Keywords (english): Hurwitz’s theorem; Pfister’s theorem on sums of squares
• Language: croatian
• URN:NBN: urn:nbn:hr:217:156569
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-09-15 11:22:44